The are no blending options in the channels palette, but is it still possible to blend? Yes, you can use Image / Apply Image, but I would like to show a different way.

In this example I have a copy of the green channel at the bottom of my channels palette. To blend this copy in overlay, I need to select the channel first with Ctrl+A (Command+C on the Mac) or in the menu: Select / All.

I then copy the image with Ctrl+C and paste it with Ctrl+V (Command+C and Command+V on the Mac).
As expected nothing happens. But it does allow us the use the fade command: Edit / Fade….

The fade command allows us to set the blending mode to overlay and after clicking on OK we’re blending the channel in overlay mode.

Note: blending channels can be very useful when you use channels to extract images from their background.